Chapter 7.  Control Charts for Attributes
Sponsored Links
This presentation is the property of its rightful owner.
1 / 59

Chapter 7. Control Charts for Attributes PowerPoint PPT Presentation


  • 112 Views
  • Uploaded on
  • Presentation posted in: General

Chapter 7. Control Charts for Attributes. Control Chart for Fraction Nonconforming. Fraction nonconforming is based on the binomial distribution. n : size of population p : probability of nonconformance D : number of products not conforming Successive products are independent.

Download Presentation

Chapter 7. Control Charts for Attributes

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 7. Control Charts for Attributes


Control Chart for Fraction Nonconforming

Fraction nonconforming is based on the binomial distribution.

n: size of population

p: probability of nonconformance

D: number of products not conforming

Successive products are independent.

Mean of D = np

Variance of D = np(1-p)


Sample fraction nonconformance


w: statistics for quality

Mean of w: μw

Variance of w: σw2

L: distance of control limit from center line (in standard deviation units)

If p is the true fraction nonconformance:


If p is not know, we estimate it from samples.

m: samples, each with n units (or observations)

Di: number of nonconforming units in sample i

Average of all observations:


Example 6-1. 6-oz cardboard cans of orange juice


If samples 15 and 23 are eliminated:


Additional samples collected after adjustment of control chart:


Control chart variables using only the recent 24 samples:

Set equal to zero for negative value


Design of Fraction Nonconforming Chart

Three parameters to be specified:

  • sample size

  • frequency of sampling

  • width of control limits

    Common to base chart on 100% inspection of all process output over time.

    Rational subgroups may also play role in determining sampling frequency.


np Control Chart


Variable Sample Size

Variable-Width Control Limits


Variable Sample Size

Control Limits Based on an Average Sample Size

Use average sample size. For previous example:


Variable Sample Size

Standard Control Chart

- Points are plotted in standard deviation units.

UCL = 3

Center line = 0

LCL = -3


Skip Section 6.2.3 pages 284 - 285


Operating Characteristic Function and Average Run Length Calculations

Probability of type II error


Since D is an integer,


Average run length

If the process is in control:

If the process is out of control


Control Charts for Nonconformities (or Defects)

Procedures with Constant Sample Size

x: number of nonconformities

c > 0: parameter of Poisson distribution

Set to zero if negative


If no standard is given, estimate c then use the following parameters:

Set to zero if negative


There are 516 defects in total of 26 samples. Thus.


There are 516 defects in total of 26 samples. Thus.

Sample 6 was due to inspection error.

Sample 20 was due to a problem in wave soldering machine.

Eliminate these two samples, and recalculate the control parameters.

New control limits:


Additional samples collected.


Further Analysis of Nonconformities


Choice of Sample Size: μ Chart

x: total nonconformities in n inspection units

u: average number of nonconformities per inspection unit


Control Charts for Nonconformities

Procedure with Variable Sample Size


Control Charts for Nonconformities

Demerit Systems: not all defects are of equal importance


ciA: number of Class A defects in ith inspection units

Similarly for ciB, ciC, and ciD for Classes B, C, and D.

di: number of demerits in inspection unit i

Constants 100, 50, 10, and 1 are demerit weights.


µi: linear combination of independent Poisson variables


Control Charts for Nonconformities

Operating Characteristic Function

x: Poisson random variable

c: true mean value

β: type II error probability


For example 6-3

Number of nonconformities is integer.


Control Charts for Nonconformities

Dealing with Low Defect Levels

  • If defect level is low, <1000 per million, c and u charts become ineffective.

  • The time-between-events control chart is more effective.

  • If the defects occur according to a Poisson distribution, the probability distribution of the time between events is the exponential distribution.

  • Constructing a time-between-events control chart is essentially equivalent to control charting an exponentially distributed variable.

  • To use normal approximation, translate exponential distribution to Weibull distribution and then approximate with normal variable


Guidelines for Implementing Control Charts

Applicable for both variable and attribute control


Determining Which Characteristics and

Where to Put Control Charts


Choosing Proper Type of Control Chart


Actions Taken to Improve Process


  • Login